The equation of the line that passes through the points (-2,0) and (0,2) can be expressed in the form y=mx+b. What is the value of m+b?
Well, if we have the equation y=mx+b, and we know that the line passes through the points (-2,0) and (0,2), we can find the values of m and b.
First, let's find the slope, m. The formula for slope, m, is given by the difference in y-coordinates divided by the difference in x-coordinates. So, m = (2-0)/(0-(-2)) = 2/2 = 1.
Next, we can plug in the coordinates of one of the points into the equation y=mx+b to find the value of b. Let's use the point (-2,0):
0 = 1*(-2) + b
0 = -2 + b
b = 2
So, we have m=1 and b=2. Therefore, m+b = 1+2 = 3.
To find the equation of the line that passes through the points (-2,0) and (0,2), we can use the slope-intercept form of a linear equation, y = mx + b, where m is the slope and b is the y-intercept.
Step 1: Find the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
For the points (-2,0) and (0,2):
m = (2 - 0) / (0 - (-2))
m = 2 / 2
m = 1
Step 2: Substitute the slope (m) into the equation: y = mx + b
Using the point (0,2):
2 = 1(0) + b
2 = b
Step 3: Substitute the value of b into the equation: y = mx + b
The equation of the line is: y = x + 2
Step 4: Find the value of m + b
m + b = 1 + 2
m + b = 3
Therefore, the value of m + b is 3.
To find the equation of a line in the form y=mx+b, we need to determine the values of m and b.
Step 1: Calculate the slope (m) of the line.
The slope is given by the formula:
m = (y₂ - y₁) / (x₂ - x₁)
Let's use the points (-2,0) and (0,2) to find the slope:
m = (2 - 0) / (0 - (-2))
m = 2 / 2
m = 1
Step 2: Use the slope (m) and one of the points (x, y) to find b.
We can choose either (-2,0) or (0,2) to substitute into the equation. Let's use (-2,0):
0 = m * (-2) + b
0 = -2 + b
b = 2
Step 3: Calculate the value of m + b.
m + b = 1 + 2
m + b = 3
Therefore, the value of m + b is 3.
the slope is (2-0)/(0+2) = 1
one of the points is the y-intercept.
So now you have both m and b; add 'em up.